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Dynamics through first-order differential equations in the configuration space

Record Type:	Electronic resources : Monograph/item
Title/Author:	Dynamics through first-order differential equations in the configuration spaceby Jaume Llibre, Rafael Ramirez, Valentin Ramírez.
Author:	Llibre, Jaume.
other author:	Ramirez, Rafael.
Published:	Cham :Springer Nature Switzerland :2023.
Description:	xxii, 345 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	DynamicsMathematics.
Online resource:	https://doi.org/10.1007/978-3-031-27095-6
ISBN:	9783031270956$q(electronic bk.)

Dynamics through first-order differential equations in the configuration space
Llibre, Jaume.

Dynamics through first-order differential equations in the configuration space[electronic resource] /by Jaume Llibre, Rafael Ramirez, Valentin Ramírez. - Cham :Springer Nature Switzerland :2023. - xxii, 345 p. :ill., digital ;24 cm.

Chapter. 1. Dynamics via the first order ordinary differential equations -- Chapter. 2. Constrained Cartesian vector fields -- Chapter. 3. Three dimensional constrained Cartesian vector fields -- Chapter. 4. Cartesian-Synge-Cinsov vector field -- Chapter. 5. Generalized Cartesian-Nambu vector fields -- Chapter. 6. Integrability of generalized Cartesian-Nambu vector fields.

The goal of this monograph is to answer the question, is it possible to solve the dynamics problem inside the configuration space instead of the phase space? By introducing a proper class of vector field - the Cartesian vector field - given in a Riemann space, the authors explore the connections between the first order ordinary differential equations (ODEs) associated to the Cartesian vector field in the configuration space of a given mechanical system and its dynamics. The result is a new perspective for studying the dynamics of mechanical systems, which allows the authors to present new cases of integrability for the Suslov and Veselova problem; establish the relation between the Cartesian vector field and the integrability of the geodesic flow in a special class of homogeneous surfaces; discuss the importance of the Nambu bracket in the study of first order ODEs; and offer a solution of the inverse problem in celestial mechanics.

ISBN: 9783031270956$q(electronic bk.)

Standard No.: 10.1007/978-3-031-27095-6doiSubjects--Topical Terms:

559162
Dynamics
--Mathematics.

LC Class. No.: TA352 / .L55 2023

Dewey Class. No.: 515.39

Dynamics through first-order differential equations in the configuration space
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245 1 0 $a Dynamics through first-order differential equations in the configuration space $h [electronic resource] / $c by Jaume Llibre, Rafael Ramirez, Valentin Ramírez.
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300 $a xxii, 345 p. : $b ill., digital ; $c 24 cm.
505 0 $a Chapter. 1. Dynamics via the first order ordinary differential equations -- Chapter. 2. Constrained Cartesian vector fields -- Chapter. 3. Three dimensional constrained Cartesian vector fields -- Chapter. 4. Cartesian-Synge-Cinsov vector field -- Chapter. 5. Generalized Cartesian-Nambu vector fields -- Chapter. 6. Integrability of generalized Cartesian-Nambu vector fields.
520 $a The goal of this monograph is to answer the question, is it possible to solve the dynamics problem inside the configuration space instead of the phase space? By introducing a proper class of vector field - the Cartesian vector field - given in a Riemann space, the authors explore the connections between the first order ordinary differential equations (ODEs) associated to the Cartesian vector field in the configuration space of a given mechanical system and its dynamics. The result is a new perspective for studying the dynamics of mechanical systems, which allows the authors to present new cases of integrability for the Suslov and Veselova problem; establish the relation between the Cartesian vector field and the integrability of the geodesic flow in a special class of homogeneous surfaces; discuss the importance of the Nambu bracket in the study of first order ODEs; and offer a solution of the inverse problem in celestial mechanics.
650 0 $a Dynamics $x Mathematics. $3 559162
650 0 $a Configuration space. $3 467965
650 0 $a Differential equations. $3 183925
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650 2 4 $a Differential Geometry. $3 273785
650 2 4 $a Mathematical Physics. $3 522725
700 1 $a Ramirez, Rafael. $3 742186
700 1 $a Ramirez, Valentin. $3 951097
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